The ability to produce patterns of single or multiple cells through precise surface engineering of cell culture substrates has promoted the development of cellular bioassays that provide entirely new insights into the factors that control cell adhesion to material surfaces, cell proliferation, differentiation and molecular signaling pathways. The ability to control shape and spreading of attached cells and cell-cell contacts through the form and dimension of the cell-adhesive patches with high precision is important. Commitment of stem cells to different specific lineages depends strongly on cell shape, implying that controlled microenvironments through engineered surfaces may not only be a valuable approach towards fundamental cell-biological studies, but also of great importance for the design of cell culture substrates for tissue engineering. Furthermore, cell patterning is an important tool for organizing cells on transducers for cell-based sensing and cell-based drug discovery concepts. From a material engineering standpoint, patterning approaches have greatly profited by combining microfabrication technologies, such as photolithography, with biochemical functionalization to present to the cells biological cues in spatially controlled regions where the background is rendered non-adhesive ("non-fouling") by suitable chemical modification. The focus of this review is on the surface engineering aspects of biologically motivated micropatterning of two-dimensional (flat) surfaces with the aim to provide an introductory overview and critical assessment of the many techniques described in the literature. In particular, the importance of non-fouling surface chemistries, the combination of hard and soft lithography with molecular assembly techniques as well as a number of less well known, but useful patterning approaches, including direct cell writing, are discussed.